Question

The decimal form of 1 /999 in non-terminating recurring

Answer 1

0.001001001...........

Answer 2

Given :  1/999

To Find : Decimal Form

Solution:

 1/999  = 1/(3 * 3 * 3 * 37)

As denominator has  prime factors other than 2 and 5 hence decimal expansion will be non terminating recurring

                       0.001          

          999 )    1.000    (

                       0

                      ___

                        10

                          0

                        ____

                          100

                              0

                         ______

                           1000

                             999

                             _____

                                  1

Remainder is repeated

Hence 1/999  = 0.001...

decimal form of 1/999   is   $0.\overline{001}$  

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